While the present invention was specifically developed for use in the commercial production of water beds, its basic utility is found in the construction or formation of relatively large water tight envelopes or bags from flexible sheet plastic material. It may also be used to form a seam joining two sheets to each other along a common edge. In essence, the water bed is simply a form of mattress which consists of a large bag or envelope of flexible water tight material filled with water. Conventionally, the envelope is constructed from flexible plastic sheet material by various techniques which almost invariably require the formation of seams. The overall dimensions of the water beds are such that a substantial volume of water, in the order of several hundred gallons, is required to completely fill the bed, which obviously requires careful attention to the avoidance of any leakage. Presently available plastic materials are sufficiently water tight and possess sufficient mechanical strength to provide adequate assurance against leakage by failure of the material itself in ordinary usage, apart from the possibility of puncture by sharp or pointed objects. Leakage problems encountered usually result from a failure of some type in the seam. The plastic sheet materials employed in the manufacture of water beds are most conveniently seamed by heat sealing or thermal bonding techniques which, because of the substantial length of the seams required, may not always achieve the optimum degree of bonding over the entire length of the seam. Because the seam can be no stronger than its weakest point, unless a high degree of care is used in the seaming process, adequate effective seam strength and integrity can be difficult to achieve consistantly.